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Generalized maximum flow over time with intermediate storage

Author

Listed:
  • Tanka Nath Dhamala

    (Tribhuvan University)

  • Mohan Chandra Adhikari

    (Tribhuvan University)

  • Durga Prasad Khanal

    (Tribhuvan University)

  • Urmila Pyakurel

    (Tribhuvan University)

Abstract

We consider two classical network flow problems. First, it is possible to store excess flow in the intermediate nodes to improve the total amount of flow that can be transported through the network. Second, we consider lossy network, where each arc has certain gain factor along with capacity and some portion of the flow is lost while traversing through such arcs. While both extensions have been considered separately in the literature, this will be the first time that they are considered simultaneously, which requires new mathematical model, analysis and solution methods. We consider that intermediate nodes have sufficient holding capacity and the excess flow is stored in the priority order within their capacity. We introduce the generalized maximum static and dynamic flow problems with intermediate storage in lossy network and present efficient algorithms and FPTAS for the solutions. Furthermore, notion of the generalized maximum dynamic flow with excess flow storage is extended to contraflow technique with symmetric and asymmetric arc travel times.

Suggested Citation

  • Tanka Nath Dhamala & Mohan Chandra Adhikari & Durga Prasad Khanal & Urmila Pyakurel, 2024. "Generalized maximum flow over time with intermediate storage," Annals of Operations Research, Springer, vol. 335(1), pages 111-134, April.
    • Handle: RePEc:spr:annopr:v:335:y:2024:i:1:d:10.1007_s10479-023-05773-w
    DOI: 10.1007/s10479-023-05773-w
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    References listed on IDEAS

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    1. Urmila Pyakurel & Stephan Dempe, 2021. "Universal Maximum Flow with Intermediate Storage for Evacuation Planning," Springer Optimization and Its Applications, in: Ilias S. Kotsireas & Anna Nagurney & Panos M. Pardalos & Arsenios Tsokas (ed.), Dynamics of Disasters, pages 229-241, Springer.
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    4. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    5. Donald Goldfarb & Zhiying Jin & James B. Orlin, 1997. "Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 793-802, November.
    6. Urmila Pyakurel & Stephan Dempe, 2020. "Network Flow with Intermediate Storage: Models and Algorithms," SN Operations Research Forum, Springer, vol. 1(4), pages 1-23, December.
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    9. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    10. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    11. Shiva Prakash Gupta & Urmila Pyakurel & Tanka Nath Dhamala, 2023. "Multi-commodity flow problem on lossy network with partial lane reversals," Annals of Operations Research, Springer, vol. 323(1), pages 45-63, April.
    12. Donald Goldfarb & Zhiying Jin, 1996. "A Faster Combinatorial Algorithm for the Generalized Circulation Problem," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 529-539, August.
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